OXFORD, Ohio — Called “our hometown hero” by Gov. John Kasich, U.S. Rep. Paul Ryan made his Ohio campaign debut on Wednesday as the Republican candidate for vice president spoke at his alma mater, Miami University of Ohio.

Looking about as youthful as he must have appeared when he graduated in 1992, the seven-term Wisconsin congressman said he welcomed a debate on Medicare and attacked the current administration as a failure. Mr. Ryan was picked on Saturday by presumed Republican nominee Mitt Romney to be his running mate.

Mr. Ryan told a crowd estimated by the Romney campaign at 5,500 people that a Romney presidency would be focused on growing jobs, and he extended the campaign’s criticism of what it sees as an “angry” tone in the Obama campaign.

“The President, I am told, is talking about Medicare today. We want this debate. We need this debate. We will win this debate,” Mr. Ryan said.

He said the President took $700 billion from Medicare to pay for his national health-care plan, and that payroll taxes were supposed to pay for only Social Security and Medicare.

“Now, because of President Obama we’re also going to pay for Obamacare,” Mr. Ryan said. “It’s not right. He knows it. He can’t defend it.”

Half of recent college graduates are working in jobs they didn’t train for, or they aren’t looking for work at all, while ever-rising tuition has left them wallowing in debt, Mr. Ryan continued.

“President Obama is out of ideas, and that’s why his campaign is based on anger and division,” he said.

Mr. Ryan, 42, graduated from Miami with a dual degree in economics and political science. He also received an honorary degree as a commencement speaker in 2009.

Among his introducers was a former economics professor, Rich Hart, who recalled Mr. Ryan stopping by his office to discuss political and economic philosophy.

“We talked about supply-side economics and the role of government in society, a limited role,” Mr. Hart said to appreciative cheers from the Republican crowd. “And we talked about the importance of individual freedom and liberty. And what I learned from these discussions and what everyone knows now is that Paul is a man of ideas, a man of vision.”

Mr. Ryan’s selection as running mate ended speculation about U.S. Sen. Rob Portman (R., Ohio) taking the No. 2 spot. Mr. Portman also introduced Mr. Ryan to the crowd, and the two embraced in a long hug. As he started to speak, Mr. Ryan said Mr. Portman gave him his “lucky buckeye” from his 2010 Senate race.

U.S. Rep. Paul Ryan (R., Wis.) told supporters at a campaign event at Miami University in Oxford, Ohio, that he and presidential hopeful Mitt Romney will not duck tough issues during their campaign.

Mr. Ryan is thought by many to be a risky choice for the Republican ticket because of the budget plan he pushed through the GOP-controlled House of Representatives as its budget committee chairman. The budget calls for changing Medicare from a single entitlement program to one that subsidizes private insurance, starting with people who are more than 10 years from retirement.

Mr. Ryan’s reminiscences of his college days included getting 14 stitches for a hockey injury and a preference for “five-way” Skyline Chili.

He sounded a call for smaller government and said public rights “come from nature and God, not from government.

“We will not duck the tough issues. We will lead. We will not blame others. We will take responsibility. And we will not try to transform or replace our founding principles. We will reapply our founding principles,” Mr. Ryan said.

The Republican candidate was also welcomed by Mr. Kasich, who said Mr. Romney and now Mr. Ryan are facing the same torrent of abuse he claimed was heaped on him by his 2010 rivals for governor.

“Paul Ryan is not a name-caller. He’s not a fabricator. He’s a person who thinks we need to stare our problems straight in the eye and have the courage to solve them. That is what our hometown hero is all about,” Mr. Kasich said.

The Romney campaign said 5,500 people were ticketed into the grassy field behind an engineering building for the 6 p.m. speech that got under way nearly a half-hour late, apparently to accommodate a long line of people waiting to be screened through two security checkpoints. Hundreds more stood outside the controlled area.

A small crowd of Obama supporters was close enough ­— closer than is usually possible at presidential campaign events — to be heard by the crowd in the rear of the venue.

Among their chants: “Outsource Romney.” A popular sign read, “Romney: Mr. 1%.”

The presidential tickets are campaigning heavily in Ohio, one of a handful of swing states that could determine the Nov. 6 election’s outcome. Mr. Romney made four stops Tuesday in southeast Ohio, while President Obama is expected back in the Buckeye State soon.

The Obama campaign said the $716 billion that Mr. Ryan cited is listed as a spending cut in Mr. Ryan’s own budget proposal, and neither plan cuts “a single guaranteed Medicare benefit.”

“It’s a shame that someone picked for his ‘strong beliefs’ is now abandoning them just to help Mr. Romney score a political point,” said Danny Kanner, Obama campaign spokesman .

The campaign cites fact-checking organizations to say that the President’s health-care reform reduces Medicare’s expected rate of growth over the next 10 years through cuts in reimbursements and payments to providers.

“The Romney-Ryan budget that now calls for the evisceration of student-loan programs and many more programs that allow students, families, and seniors an opportunity at better lives brings about a cruel irony. As Congressman Ryan took all advantages of these programs at a critical juncture in his life, he now wants to deny them to current and future generations of Americans, all in the name of offering irresponsible tax cuts to the wealthiest among us,” Mr. Sizemore’s statement said.

Miami is a state-supported institution of about 16,000 students.

The university said that Mr. Ryan continues Miami’s legacy of national public service, which includes Benjamin Harrison, an 1852 graduate who was president from 1889 to 1893, and Whitelaw Reid, Harrison’s running mate in a reelection bid, who graduated in 1856.

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